E?
Keely
"The magnetic or electric forces of the earth are thus kept in stable equilibrium by this triune force, and the chords of this force may be expressed as 1st, the dominant, 2nd, the harmonic, and 3rd, the enharmonic. The value of each is, one to the other, in the rates of figures, true thirds. E flat- transmissive chord or dominant; A flat- harmonic; A double flat- enharmonic." [Vibratory Physics - The Connecting Link between Mind and Matter]
"In analyzing this triple union in its vibratory philosophy, I find the highest order of perfection in this assimilative action of Nature. The whole condition is atomic, and is the introductory one which has an affinity for terrestrial centres, uniting magnetically with the Polar stream, in other words, uniting with the Polar stream by neutral affinity. The magnetic or electric forces of the earth are thus kept in stable equilibrium by this triune force, and the chords of this force may be expressed as 1st, the dominant, 2nd, the harmonic, and 3rd, the enharmonic. The value of each is, one to the other, in the rates of figures, true thirds. E?, - transmissive chord or dominant; A? - harmonic; A?? - enharmonic. The unition of the two prime thirds is so rapid, when the negative and the positive conditions reach a certain range of vibratory motion, as to be compared to an explosion. During this action the positive electric stream is liberated, and immediately seeks its neutral terrestrial centre, or centre of highest attraction." [True Science]
"The experiment illustrating "chord of mass" sympathy was repeated, using a glass chamber, 40 inches in height, filled with water, standing on a slab of glass. Three metal spheres, weighing about 6 ounces each, rested on the glass floor. The chord of mass of these spheres was B flat first octave, E flat second octave and B flat third octave. Upon sounding the note B flat on the sympathetic transmitter, the sphere having that chord of mass rose slowly to the top of the chamber, the positive end of the wire having been attached, which connected the covered jar with the transmitter. The same result followed the sound of the other spheres, all of which descended as gently as they rose, upon changing the positive to the negative. J.M. Wilcox, who was present remarked: "This experiment proves the truth of a fundamental law in scholastic philosophy, that when one body attracts or seeks another body, it is not that the effect is the sum of the effects produced by parts of one body upon parts of another, one aggregate of effects, but the result of the operation of one whole upon another whole." [KEELYS SECRETS - 1888]
"The relations of the components of the electric streams are: Dominant E flat, harmonic A flat, enharmonic C double flat.
"The keynote of electromagnetic sympathy in "transmissive combinations" is:
"THIRDS ON FIRST OCTAVE SUBDIVISION B FLAT DIATONIC
"SIXTHS ON SAME SUBDIVISION OF THIRDS OCTAVE HARMONIC
"NINTHS ON SAME SUBDIVISION OF SIXTHS OCTAVE ENHARMONIC [Snell Manuscript]
Ramsay
The triplet B, D, F, has been called the imperfect triad, because in it the two diatonic semitones, B-C and E-F, and the two minor thirds which they constitute, come together in this so-called imperfect fifth. But instead of deserving any name indicating imperfection, this most interesting triad is the Diatonic germ of the chromatic chord, and of the chromatic system of chords. Place this triad to precede the tonic chord of the key of C major, and there are two semitonic progressions. Place it to precede the tonic chord of the key of F# major, and there are three semitonic progressions. Again, if we place it to precede the tonic chord of the key of A minor, there are two semitonic progressions; but make it precede the tonic chord of E? minor, and there are three semitonic progressions. This shows that the chromatic chord has its germ in, and its outgrowth from the so-called "natural notes," that is notes without flats or sharps, notes with white keys; and that these natural notes furnish, with only the addition of either A? from the major scale or G# from the minor, a full chromatic chord for one major and one minor chord, and a secondary chromatic chord for one more in each mode. [Scientific Basis and Build of Music, page 52]
In the same way, but inversely, and still under the Law of Duality, the middle of the subdominant minor is lowered a flat. F#67 1/2 in the key of E minor is F64 in the key of A; B45 in the key of A is B?42 2/3 in the key of D; E60 in the key of D is E?56 8/9 in the key of G. This lowering by flats of the subdominant middle in the minors, responsive to the raising by sharps of the dominant middle in the majors, goes on through all the twelve minor keys.1 [Scientific Basis and Build of Music, page 62]
G# as it occurs in the scales of A, E, and B major, and A? as it occurs in the scales of F and B? minor, are only distant the apotome minor, and are well represented by one key of the piano. It is only G# as it occurs in the scale of F six sharps major, and A? as it occurs in the scale of E six flats minor, that is not represented on the piano. These two extreme notes F# and E? minor are at the distance of fifteenth fifths and a minor third from each other. This supplies notes for 13 major and 13 minor mathematical scales; but as this is not required for our musical world of twelve scales, so these far-distant G# and A? are not required. The piano is only responsible for the amount of tempering which twelve fifths require, and that is never more than one comma and the apotome minor. [Scientific Basis and Build of Music, page 80]
The reason why there are 13 mathematical scales is that G? and F# are written separately as two scales, although the one is only a comma and the apotome minor higher than the other, while in the regular succession of scales the one is always 5 notes higher than the other; so this G? is an anomaly among scales, unless viewed as the first of a second cycle of keys, which it really is; and all the notes of all the scales of this second cycle are equally a comma and the apotome higher than the notes of the first cycle; and when followed out we find that a third cycle is raised just as much higher than the second as the second is higher than the first; and what is true of these majors may be simply repeated as to the D# and E? of the minors, and the new cycle so begun, and all successive minor cycles. Twelve and not thirteen is the natural number for the mathematical scales, which go on in a spiral line, as truly as for the tempered scales, which close as a circle at this point. [Scientific Basis and Build of Music, page 89]
In a similar and responsive way Duality provides for the six major scales with flats.
The two new notes required for the scale of
F major are the B? of D, and the D of A minor;
for B? major, the E? of G, and the G of D minor;
for E? major, the A? of C, and the C of G minor;
for A? major, the D? of F, and the F of C minor;
for D? major, the G? of B?, and the B? of F minor;
for G? major, the C? of E?, and the E? of B? minor.1 [Scientific Basis and Build of Music, page 90]
sexual note in the scales of G major and E minor are the two A's; in D major and B minor, the two E's; in A major and F# minor, the two B's; in E major and C# minor, the two F's; in B major and G# minor, the two C's; and in F# major and D# minor, the two G's. These two last scales being the beginning of a second cycle of twelve scales when the scales are written half in flats and half in sharps, as we have done them in this case. Turning to the other half of our circle, those which we have, and which usually in music books are, written in flats, in F major and D minor the sexual notes are the two G's; in B? and G, the two C's, in E? and C, the two F's; in A? and F, the two B's; in D? and B?, the two E's; and in G? and E?, the two A's. [Scientific Basis and Build of Music, page 91]
This tune is in the key of E? Major, and the key into which it moves for a passage is the next above it, B? Major. The first chord, E? G B?, is the tonic; the second and third are the tonic and dominant; the fourth, C E? G, whose full form would be C E? G B?, is the compound subdominant of the new key, which suggests the approaching modulation. The next two chords, in which the measure closes, may either be viewed as the tonic and dominant of the key, or the subdominant and tonic of the new key. The second measure opens with the same chord which closes the first measure, and is best defined as the tonic of the new key; the second chord is clearly the dominant of the new key, and the whole of the second measure is in the new key, and reads, T. D. S. T. compound D. T. Some of these chords might be read as chords of the old key, so near to each other and so kindred are the contiguous keys. All contiguous keys to a certain extent overlap each other, so that some of the chords may be variously read as belonging to the one or to the other. [Scientific Basis and Build of Music, page 94]
The middle portion with the zigzag and perpendicular lines are the chromatic chords, as it were arpeggio'd. They are shown 5-fold, and have their major form from the right side, and their minor form from the left. In the column on the right they are seen in resolution, in their primary and fullest manner, with the 12 minors. The reason why there are 13 scales, though called the 12, is that F# is one scale and G? another on the major side; and D# and E? separated the same way on the minor side. Twelve, however, is the natural number for the mathematical scales as well as the tempered ones. But as the mathematical scales roll on in cycles, F# is mathematically the first of a new cycle, and all the notes of the scale of F# are a comma and the apotome minor higher than G?. And so also it is on the minor side, D# is a comma and the apotome higher than E?. These two thirteenth keys are therefore simply a repetition of the two first; a fourteenth would be a repetition of the second; and so on all through till a second cycle of twelve would be completed; and the thirteenth to it would be just the first of a third cycle a comma and the apotome minor higher than the second, and so on ad infinitum. In the tempered scales F# and G? on the major side are made one; and D# and E? on the minor side the same; and the circle of the twelve is closed. This is the explanation of the thirteen in any of the plates being called twelve. The perpendicular lines join identical notes with diverse names. The zigzag lines thread the rising Fifths which constitute the chromatic chords under diverse names, and these chords are then seen in stave-notation, or the major and minor sides opposites. The system of the Secondary and Tertiary manner of resolution might be shown in the same way, thus exhibiting 72 resolutions into Tonic chords. But the Chromatic chord can also be used to resolve to the Subdominant and Dominant chords of each of these 24 keys, which will exhibit 48 more chromatic resolutions; and resolving into the 48 chords in the primary, secondary, and tertiary manners, will make 144 resolutions, which with 72 above make 216 resolutions. These have been worked out by our author in the Common Notation, in a variety of positions and inversions, and may be published, perhaps, in a second edition of this work, or in a practical work by themselves. [Scientific Basis and Build of Music, page 115]
These two plates show the chromatic chord resolving into the twelve major and twelve minor tonic chords of the twenty-four scales. There seems to be twenty-five, but that arises from making G? and F# in the major two scales, whereas they are really only one; and the same in the minor series, E? and D# are really one scale. C in the major and A in the minor, which occur in the middle of the series, when both sharps and flats are employed in the signatures, are placed below and outside of the circular stave to give them prominence as the types of the scale; and the first chromatic chord is seen with them in its major and minor form, and its typical manner of resolving - the major form rising to the root, and falling to the top and middle; the minor form falling to the top, and rising to the root and middle. The signatures of the keys are given under the stave. [Scientific Basis and Build of Music, page 116]
advance by semitones, the keys with ?s and #s alternate in both modes. The open between G# and A? in the major, and between D# and E? in the minor, is closed in each mode, and the scale made one. The dotted lines across the plate lead from major to relative minor; and the solid spiral line starting from C, and winding left and right, touches the consecutive keys as they advance normally, because genetically, by fifths. The relative major and minor are in one ellipse at C and A; and in the ellipse right opposite this the relative to F# is D#, and that of G? and E?, all in the same ellipse, and by one set of notes, but read, of course, both ways. [Scientific Basis and Build of Music, page 117]
The inner stave contains the chromatic scale of twelve notes as played on keyed instruments. The flat and sharp phase of the intermediate notes are both given to indicate their relation to each other; the sharpened note being always the higher one, although seemingly on the stave the lower one. The two notes are the apotome minor apart overlapping each other by so much; ?D is the apotome lower than C#; ?E the apotome lower than D#; F# the apotome higher than ?G; G# the apotome higher than ?A; and A# the apotome higher than ?B. The figures for the chromatic scale are only given for the notes and their sharps; but in the mathematical series of notes the numbers are all given. [Scientific Basis and Build of Music, page 120]
Hughes
The difference in the development of a major and a minor harmony
—The twelve developing keys mingled
—D? shown to be an imperfect minor harmony
—E? taking B? as C? to be the same as D#
—The intermediate tones of the seven white notes are coloured, showing gradual modulation
—As in the diagram of the majors, the secondaries are written in musical clef below the primaries, each minor primary sounding the secondaries of the third harmony below, but in a different order, and one tone rising higher, . . . . . 34 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]
Minor key-notes developing by sevens, veering round and in musical clef below
—The use of the two poles D#-E? is seen, . . . . . . . . . . 35 [Harmonies of Tones and Colours, Table of Contents3 - Harmonies]
I had forgotten all the minor keys, except that A is the relative minor of C major; but although I had only faint hopes of success, I determined to try, and I gained the twelve keys correctly, with the thirteenth octave. I found also that E? was usually printed as a minor key-note, Nature's laws having shown that it must be D#. [Harmonies of Tones and Colours, Dr. Gauntletts Remarks1, page 13]
When the twelve minor harmonies are traced developing in succession, we notice how exactly they all agree in their method of development, also the use of the chasms and the double tones, the seven of each harmony rising a tone when ascending, but reversing the movement in descending; keys with sharps and those with flats are mingled. The intermediate tones are here coloured, showing gradual modulation. D? is shown to be an imperfect minor harmony, and E?, by employing B as C?, is seen to be equivalent to D#. [Harmonies of Tones and Colours, Diagram IX - The Minor Keynote A and Its Six Notes, page 34a]
The diagram represents the Minor Key-note A and its 6 notes veering round in trinities; A and the other 11 developing their trinities in musical clef. Below each is the order in which the pairs unite, avoiding consecutive fifths, Lastly, D? is shewn to be an imperfect minor harmony, and by employing B as C?, E? is seen to be the same harmony as D#. As before, it should be remembered that the sharp and flat notes should, strictly, have intermediate tints. [Harmonies of Tones and Colours, The Diagram Represents the Minor Keynote, page 34c]
Below, the D# and E? are repeated, to shew the use of the two poles. [Harmonies of Tones and Colours, First Circle are 7 Minor Keynotes, page 35c]
THE same laws are followed here as in the development of the major scales. In that of A, F, the sixth note, has risen to F#, in order to meet B, which has previously sounded. In descending, the seventh note, B, falls to B?, in order to meet F, which has also previously sounded. The notes, ascending or descending, always follow the harmony of their key-note, except when rising higher or falling lower to meet in fifths. We may here trace the twelve, the ascending scale sounding the fifth harmony higher than its key-note, and, in descending, sounding the fifth lower harmony. The four pairs of each scale are written at the end of the lines. If we strike the twelve scales as they follow in succession, the thirteenth note being the octave of the first, and leader of a higher twelve; having gained them six times, at the seventh they gradually rise (though beyond the power of a keyed instrument) into the higher series of seven octaves, and again, in descending, they fall lower, and are linked into the lower series of seven octaves. Nine notes of any ascending minor scale may be struck without the necessity of modulating beyond the fifth harmony. For example, in the scale of A, its tenth note, C#, rises to meet the sixth note, which has previously sounded. In descending, E?, the eleventh note, meets B?, the seventh note, which has previously sounded. The scale of A may be traced veering round by reference to Diagram IX., beginning with A, and carrying the four lowest notes an octave higher, F rising to F# in ascending, B falling to B? in descending. [Harmonies of Tones and Colours, Diagram XI - The Twelve Minor Keynotes with the Six Note of Each, page 36a]
ALTHOUGH only twelve notes of a keyed instrument develope perfect minor harmonics, there are fifteen different chords, the double tones D#-E?, E#-F?, A#-B? all sounding as roots. The fifteen roots are written in musical clef. A major and a minor fifth embrace the same number of key-notes, but the division into threefold chords is different. In counting the twelve, a major fifth has four below the third note of its harmony, and three above it; a minor fifth has three below the third note of its harmony, and four above it. A major seventh includes twelve key-notes, a minor seventh only eleven. As an example of the minor chords in the different keys, we may first examine those in the key of A, written in musical clef. The seven of its harmony have two threefold chords, and two of its ascending scale. If we include the octave note, the highest chord of the descending scale is a repetition (sounding an octave higher) of the lowest chord of the seven in its harmony, and the second chord of the descending scale is a repetition of the first chord of its ascending scale. These two repetition chords are only written to the key of A: the chords of the other eleven keys will all be found exactly to agree with those of A in their mode of development. We may again remark on the beautiful effect which would result if the colours of the minor chords could be seen, with the tones, as they develope. [Harmonies of Tones and Colours, Diagram XII - The Chords of the Twelve Minor Keys, page 37a]
See Also